# The Elements of Plane and Solid Geometry ...

D. Van Nostrand Company, 1890 - Geometry - 393 pages
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### Contents

 INTRODUCTION 1 Angular Measure 8 PLANE GEOMETRY 14 Parallel Lines 23 Triangles 33 Quadrilaterals 46 Polygons 53 Symmetry 64
 The Measure of the Circle 215 Problems of Construction 224 Value of n Method of Perimeters 231 Exercises Theorems 243 Definitions 250 Parallel Planes 258 Diedral Angles Definitions 264 Polyedral Angles Definitions 276

 BOOK II 74 Relative Position of Two Circles 88 Quadrilaterals 102 Exercises Theorems 123 SIMILAR FIGURES 134 Proportional Lines 143 Similar Figures 149 Similar Polygous 155 Problems of Construction 168 Exercises Theorems 175 Comparison of Areas 187 Applications 200 BOOK V 208
 Exercises Theorems 282 Pyramids 302 Similar Polyedrons 316 General Properties of Polyedrons 325 BOOK VIII 334 Spherical Triangles and Polygons 342 Polar Triangles 349 Exercises Theorems 360 BOOK IX 366 The Sphere 378 Exercises Theorems 386 Copyright

### Popular passages

Page 72 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Page 186 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Page 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Page 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.
Page 378 - The circumferences of the sections made by the planes are called the bases of the zone, and the distance between the planes is the altitude of the zone.
Page 354 - A zone is a portion of the surface of a sphere included between two parallel planes. The circumferences of the sections...
Page 29 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 220 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R